For convenience of the reader, we first provide necessary notions from the theory of differential equations with \(\Delta \) -derivative [1]}, [2]}. Let \(T\)  be a closed subset of the real line.
Define on \(T\)  the jump functions \(\sigma \)  and \(\sigma _-\)  in the following way:
\(\sigma (x):=\left\lbrace \begin{array}{cl}\inf \lbrace s\in T:\; s>x\rbrace , & x\ne \max T,\\[2mm]\max T, & x=\max T,\end{array}\right.\) 
\(\sigma _-(x):=\left\lbrace \begin{array}{cl}\sup \lbrace s\in T:\; s<x\rbrace , & x\ne \min T,\\[2mm]\min T, & x=\min T.\end{array}\right.\) 
